Asked if he would say sorry to those facing unexpected bills, Mr Hartnett told BBC Radio 4's Money Box programme: "I'm not sure I see a need to apologise.

"I've read the papers, listened to the media and heard stories of HMRC blunder and IT failure – neither of those are true.

"Every country that I know of that has deduction of tax from wages and salaries has to do a reconciliation at the end of each year and we're doing one."

He added: "I don't think we are extraordinary. Once or twice in the past the numbers have been very large – sometimes they're less – it depends on how the system has been operated and what issues there have been."

"We didn't get it wrong. This needs to be reconciled."

People who owe less than £2,000 will be able to pay the money in monthly instalments taken from their salary over one to three years but those owing more will have no more than three months to return the cash.

Mr Hartnett indicated that around 45,000 letters had been sent out as an initial pilot – with changes potentially being made before the rest of the six million people who owe tax or are due refunds received theirs – due before Christmas.

Mr Hartnett said he had "no plan to resign over this.

"I am addressing the issue and I think the nation needs me to do just that."